The (2k-1)-connected multigraphs with at most k-1 disjoint cycles
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In 1963, Corradi and Hajnal proved that for all k≥1 and n≥3k, every (simple) graph G on n vertices with minimum degree δ(G)≥2k contains k disjoint cycles. The same year, Dirac described the 3-connected multigraphs not containing two disjoint cycles and asked the more general question: Which (2k—1)-connected multigraphs do not contain k disjoint cycles? Recently, the authors characterized the simple graphs G with minimum degree δ(G)≥2k—1 that do not contain k disjoint cycles. We use this result to answer Dirac's question in full.
Mathematics Subject Classification (2000)05C15 05C35 05C40
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- H. A. Kierstead, A. V. Kostochka and E. C. Yeager: On the Corradi-Hajnal Theorem and a question of Dirac, submitted.Google Scholar